Philosophy Now Forum

Think about it.

PhilX

42.

Philosophy Explorer wrote:Think about it.

PhilX

Your phone number.

Hobbes' Choice wrote:

Philosophy Explorer wrote:Think about it.

PhilX

Your phone number.

Wrong. Try again and use some logic.

PhilX

Arising_uk wrote:42.

Keep trying.

PhilX

It can't be a positive integer, for the well-known reason that if there were an uninteresting positive integer, there would be a least such; and that itself would make it interesting.

My vote would go to any noncomputable real number. The fact that noncomputable numbers exist is interesting. These are numbers whose decimal digits can not possibly be generated by any algorithm. They're random bitstrings, also known as random reals.

No particular random real can be interesting; for the reason that no random real can be characterized by any property at all.

For example the number pi, even though it's irrational and has an endless, nonrepeating decimal representation, is still computable. It can be described in finitely many symbols by the expression, "The ratio of a circle's circumference to its diameter in Euclidean geometry," and its decimal digits can be cranked out to any desired length (given sufficient computational resources) such as the famous Leibniz formula pi/4 = 1 - 1/3 + 1/5 - 1/7 + ... https://en.wikipedia.org/wiki/Leibniz_f ... for_%CF%80

There are uncountably many random reals. They are points on the number line that can not be described by algorithms. Any one of them has nothing interesting about it at all. It has no properties that distinguish it from any other.

wtf wrote:It can't be a positive integer, for the well-known reason that if there were an uninteresting positive integer, there would be a least such; and that itself would make it interesting.

My vote would go to any noncomputable real number. The fact that noncomputable numbers (numbers whose decimal digits can not possibly be generated by any algorithm; essentially random bitstrings) exist is interesting.

But no particular random real (synonym for noncomputable real) can be interesting; for the reason that no random real can be characterized by any property at all.

For example the number pi, even though it's irrational and has an endless, nonrepeating decimal representation, is still computable. It can be described in finitely many symbols by the expression, "The ratio of a circle's circumference to its diameter in Euclidean geometry," and its decimal digits can be cranked out to any desired length (given sufficient computational resources) such as the famous Leibniz formula pi/4 = 1 - 1/3 + 1/5 - 1/7 + ... https://en.wikipedia.org/wiki/Leibniz_f ... for_%CF%80

There are uncountably many random reals. They are points on the number line that can not be described by algorithms. Any one of them has nothing interesting about it at all. It has no properties that distinguish it from any other.

The answer is there is no such number. Google my question and read Wikipedia.

PhilX

Philosophy Explorer wrote: The answer is there is no such number. Google my question and read Wikipedia.

PhilX

Did I not state and acknowledge that argument in my first paragraph; then go beyond it to demonstrate that there are many uninteresting real numbers?

wtf wrote:

Philosophy Explorer wrote: The answer is there is no such number. Google my question and read Wikipedia.

PhilX

Did I not state and acknowledge that argument in my first paragraph; then go beyond it to demonstrate that there are many uninteresting real numbers?

Because you state it doesn't make it so. Because the act of identifying a number as being uninteresting makes it interesting which agrees with Wiki.

PhilX

Philosophy Explorer wrote:

wtf wrote:

Philosophy Explorer wrote: The answer is there is no such number. Google my question and read Wikipedia.

PhilX

Did I not state and acknowledge that argument in my first paragraph; then go beyond it to demonstrate that there are many uninteresting real numbers?

Because you state it doesn't make it so. Because the act of identifying a number as being uninteresting makes it interesting which agrees with Wiki.

Are you missing the point that I have not specified any number? I have described an uncountably infinite class of numbers, each one of which can't possibly be described. I could not identify or pick out any one of those numbers even if I wanted to. That's why none of them can be interesting. Not a single one of them has any distinguishing properties whatsoever.

Do you understand this example?

Computable numbers were described by Turing in his famous paper of 1936 in which he first described Turing machines. He described how a computable number was one whose digits could be calculated by his model of an abstract computer; which is still to this day the standard abstract model of what can be computed.

In the set of real numbers; that is, the collection of points on the number line; most of the numbers are non-computable. Their digits can not be generated by an algorithm. These are numbers whose description lies in the realm beyond what algorithms can do.

Any such noncomputable number can have no identifiable properties at all. It can't be selected, except by a random process. So if I randomly "throw a dart at the real line," then I have selected some random real number. Now you might regard it as interesting that I happened to hit that number and not some other. But in this case the "interestingness" derives from the fact that I selected this number by pure random chance. There is nothing about this number that distinguishes it from any other noncomputable number.

wtf wrote:
Are you missing the point that I have not specified any number? I have described an uncountably infinite class of numbers, each one of which can't possibly be described. I could not identify or pick out any one of those numbers even if I wanted to. That's why none of them can be interesting. Not a single one of them has any distinguishing properties whatsoever.

Do you understand this example?

Kronecker, the doubter, would say that any noncomputable number doesn't exist. And if it doesn't exist, then we have nothing to talk about. So with those class of numbers (if they are numbers), it wouldn't make sense to say whether or not they're uninteresting.

PhilX

Philosophy Explorer wrote:

wtf wrote:
Are you missing the point that I have not specified any number? I have described an uncountably infinite class of numbers, each one of which can't possibly be described. I could not identify or pick out any one of those numbers even if I wanted to. That's why none of them can be interesting. Not a single one of them has any distinguishing properties whatsoever.

Do you understand this example?

Kronecker, the doubter, would say that any noncomputable number doesn't exist. And if it doesn't exist, then we have nothing to talk about. So with those class of numbers (if they are numbers), it wouldn't make sense to say whether or not they're uninteresting.

PhilX

If you're arguing a constructivist, finitist, or ultra-finitist position, there's not much to discuss. You deny the set of real numbers, good for you. Euclid says he has a line? You say, No you don't. There are no lines. There is no geometry. In calculus, the Intermediate Value theorem is false. You can cross from one side of a line to the other without intersecting the line. You just drive through one of the uncountably many noncomputable holes where there should be points but you claim there aren't.

Better toss out most of modern science, which is based on the mathematical theory of the real numbers. Denying the real numbers is scientific nihilism. I couldn't talk you out of it, but you'd be virtually alone.

Are you under the historical impression that eighty or whatever years ago, mathematicians all said, "Of course! Kronecker is right. We should all find another line of work!" Is this the idea you're laboring under? Or have you in fact not really given the matter much thought at all, and just happen to have a Kronecker datapoint in your brain that you are tossing out in the hopes that it means something?

wtf wrote:

Philosophy Explorer wrote:

wtf wrote:
Are you missing the point that I have not specified any number? I have described an uncountably infinite class of numbers, each one of which can't possibly be described. I could not identify or pick out any one of those numbers even if I wanted to. That's why none of them can be interesting. Not a single one of them has any distinguishing properties whatsoever.

Do you understand this example?

Kronecker, the doubter, would say that any noncomputable number doesn't exist. And if it doesn't exist, then we have nothing to talk about. So with those class of numbers (if they are numbers), it wouldn't make sense to say whether or not they're uninteresting.

PhilX

If you're arguing a constructivist, finitist, or ultra-finitist position, there's not much to discuss. You deny the set of real numbers, good for you. Euclid says he has a line? You say, No you don't. There are no lines. There is no geometry. In calculus, the Intermediate Value theorem is false. You can cross from one side of a line to the other without intersecting the line. You just drive through one of the uncountably many noncomputable holes where there should be points but you claim there aren't.

Better toss out most of modern science, which is based on the mathematical theory of the real numbers. Denying the real numbers is scientific nihilism. I couldn't talk you out of it, but you'd be virtually alone.

I'm not denying real numbers, but pointing out a logical weakness to your position. What I'm saying is that as soon as you're saying a number is uninteresting, then you're automatically saying it is interesting (and one of the reasons why nobody should be bored). For me I accept irrational and transcendental numbers because the axioms of algebra do apply to them.

Even if I can't see the whole number doesn't mean I don't reject it. The same with black holes, e.g., because there is plenty of indirect evidence to support their existence.

PhilX

Philosophy Explorer wrote:
I'm not denying real numbers

That's exactly what you appear to be doing if you are arguing any version of constructivism/finitism.

Philosophy Explorer wrote: but pointing out a logical weakness to your position.

I don't see it.

Philosophy Explorer wrote: What I'm saying is that as soon as you're saying a number is uninteresting, then you're automatically saying it is interesting (and one of the reasons why nobody should be bored).

That argument is about positive integers, which are well-ordered. Picking out something completely randomly doesn't make it interesting. The ONLY way to choose a noncomputable number is randomly.

Philosophy Explorer wrote: For me I accept irrational and transcendental numbers because the axioms of algebra do apply to them.

If you accept irrational numbers then among those are the noncomputable numbers.

Philosophy Explorer wrote: Even if I can't see the whole number doesn't mean I don't reject it. The same with black holes, e.g., because there is plenty of indirect evidence to support their existence.

Not following the point of that remark.

Ok here is a thought experiment. You have a big bowl of identical ping-pong balls in a completely dark room. You stick your hand into the bowl and randomly choose a particular ping-pong balls. Is that ping-pong ball interesting purely by virtue of having been chosen randomly? This is really the crux of my argument, I don't have to talk about real numbers. Only about randomly choosing among indistinguishable alternatives.

Philosophy Explorer wrote:

Arising_uk wrote:42.

Keep trying.

PhilX

Nope. That is the most uninteresting number, Douglas said so.